User:Phlsph7/Formal semantics - In various fields
In various fields
[edit]Formal logic
[edit]Formal logic studies the laws of deductive reasoning, focusing on entailment relations between premises and conclusions rather than linguistic meaning in general. It investigates rules of inference, such as modus ponens, which describe the logical structure of deductively valid arguments.[1] Formal logicians develop artificial languages, like the language of predicate logic, to avoid the ambiguities of natural language and give precise descriptions of the laws of logic.[2] Formal semantics plays a central role in this endeavor for applying these laws to natural language arguments. It helps logicians discern the logical form of everyday arguments, serving as a crucial step in translating them into logical formulas.[3]
Another key overlap between formal semantics and formal logic concerns the meaning of artificial logical languages. The semantics of logic examines the construction of mathematical models of formal languages, similar to the models used by formal semanticists to study natural language. These models typically include abstract objects to represent individuals and sets. The relation to formulas is established through an interpretation function that maps symbols to the abstract objects they denote.[4] A key aspect of this interface is the contrast between syntactic and semantic entailment.[a] A premise syntactically entails a conclusion if the conclusion can be deduced using rules of inference. A premise semantically entails a conclusion if the conclusion is true in every possible model where the premise is true.[6]
Computer science
[edit]Computational semantics is an interdisciplinary field at the intersection of computer science and formal semantics. It studies how computational processes can be utilized to deal with linguistic meaning. A primary focus is the analysis of natural language sentences through computer-based methods to discern their logical structure, understand their content, and extract information. This form of inquiry has various applications in areas of artificial intelligence, such as automated reasoning, machine learning, and machine translation. Difficulties in this process come from the ambiguity, vagueness, and context dependence of natural language expressions.[7]
Another intersection concerns the analysis of the meaning of programming languages, such as C++, Python, and JavaScript. A programming language is an artificial language designed to give instructions or describe computations to be performed by computers. A formal semantics of a programming language is a mathematical model of how it works. Its goal is to help computer scientists understand, analyze, and verify program behavior.[8] Static semantics describes the process of compilation or how a human-readable programming language is translated into binary machine code.[9] Dynamic semantics examines run-time behavior or what happens during the execution of instructions.[10] The main approaches to dynamic semantics are denotational, axiomatic, and operational semantics. Denotational semantics describes the effects of code elements, axiomatic semantics examines the conditions before and after code execution, and operational semantics interprets code execution as a series of state transitions.[11]
Cognitive science
[edit]Cognitive science studies the mind by focusing on how it represents and transforms information. It is an interdisciplinary field that integrates research from diverse areas, ranging from psychology and neuroscience to philosophy, artificial intelligence, and linguistics.[12] Some researchers emphasize the central role of language in understanding the human mind and rely on formal semantics to provide an abstract model for analyzing how linguistic meaning is constructed and interpreted.[13]
Formal semantics is also relevant to cognitive neuroscience, which seeks to explain the biological processes underlying cognition. One approach uses brain imaging techniques to visualize brain activity and employs mathematical models to link this data to cognitive processes. Insights from formal semantics can refine these models and help formulate testable predictions. For instance, researchers can examine semantic cognition by presenting a person with semantic variations of a sentence and measuring the differences in brain responses.[14]
References
[edit]Notes
[edit]Citations
[edit]- ^
- Hintikka & Sandu 2006, pp. 13–14
- Audi 1999, pp. 679–681
- Cannon 2002, pp. 14–15
- ^
- Tully 2005, pp. 532–533
- Hodges 2005, pp. 533–536
- Walton 1996
- Johnson 1999, pp. 265–268
- ^
- Portner 2005, pp. 214–217
- Brun 2003, p. 83, 175, 207
- Peregrin & Svoboda 2016, pp. 55, 64
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- Cook 2009, pp. 124, 256
- Shapiro & Kouri Kissel 2024, Lead section, § 4. Semantics
- Barba 2007, pp. 639
- ^
- ^
- Forster 2003, p. 74
- Cook 2009, pp. 82, 176
- McKeon 2010, pp. 1–2, 24–25
- Shapiro & Kouri Kissel 2024, Lead section, § 5. Meta-theory
- ^
- Portner 2005, pp. 214–217
- Geeraerts 2010, p. 118
- Bunt & Muskens 1999, pp. 1–2
- Erk 2018, Summary
- Stone 2016, pp. 775–777, 799–800
- ^
- Fernández 2014, pp. 14–16
- Winskel 1993, pp. xv–xvi
- Portner 2005, pp. 214–217
- ^
- Fernández 2014, pp. 14–15
- Fritzson 2010, p. 703
- Mosses 2003, p. 167
- ^
- Fernández 2014, pp. 15–16
- Fritzson 2010, p. 703
- Mosses 2003, p. 167
- ^
- Fernández 2014, p. 16
- O’Regan 2020, pp. 193–194
- Winskel 1993, pp. xv–xvi
- ^ Portner 2005, pp. 216–217
- ^
- Portner 2005, pp. 214–217
- Partee 2008, p. 10
- Partee 1995, pp. 311–360
- ^
- Winter 2016, pp. 3–4
- Baggio, Stenning & van Lambalgen 2016, pp. 756–757, 761–762, 773–774
Sources
[edit]- Baggio, Giosuè; Stenning, Keith; van Lambalgen, Michiel (2016). "24. Semantics and Cognition". In Aloni, Maria; Dekker, Paul (eds.). The Cambridge Handbook of Formal Semantics. Cambridge University Press. pp. 756–774. ISBN 978-1-316-55273-5.
- Stone, Matthew (2016). "25. Semantics and Computation". In Aloni, Maria; Dekker, Paul (eds.). The Cambridge Handbook of Formal Semantics. Cambridge University Press. pp. 775–800. ISBN 978-1-316-55273-5.
- Winskel, Glynn (1993). The Formal Semantics of Programming Languages: An Introduction. MIT Press. ISBN 978-0-262-23169-5.
- Partee, Barbara H. (2008). Compositionality in Formal Semantics: Selected Papers. John Wiley & Sons. ISBN 978-0-470-75129-9.
- Partee, Barbara H. (1995). "11. Lexical Semantics and Compositionality". In Osherson, Daniel N.; Gleitman, Lila R. (eds.). An Invitation to Cognitive Science: Language. MIT Press. ISBN 978-0-262-65044-1.
- McKeon, Matthew. "Logical Consequence". Internet Encyclopedia of Philosophy. Retrieved 12 June 2025.
- Forster, Thomas (2003). Logic, Induction and Sets. Cambridge University Press. ISBN 978-0-521-53361-4.
- McKeon, Matthew W. (2010). The Concept of Logical Consequence: An Introduction to Philosophical Logic. Peter Lang. ISBN 978-1-4331-0645-3.
- Shapiro, Stewart; Kouri Kissel, Teresa (2024). "Classical Logic". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 12 June 2025.